Conditions for the cosmological viability of f(R) dark energy models
We derive the conditions under which dark energy models whose Lagrangian densities f are written in terms of the Ricci scalar R are cosmologically viable. We show that the cosmological behavior of f(R) models can be understood by a geometrical approach consisting in studying the m(r) curve on the (r...
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| Main Author: | |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
2007
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| In: |
Arxiv
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| Online Access: | Verlag, kostenfrei, Volltext: http://arxiv.org/abs/gr-qc/0612180
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| Author Notes: | Luca Amendola, INAF/Osservatorio Astronomico di Roma, Via Frascati 33, 00040 Monte Porzio Catone (Roma), Italy; Radouane Gannouji and David Polarski, LPTA, Universite Montpellier II, CNRS, 34095 Montpellier Cedex 05, France; Shinji Tsujikawa, Department of Physics, Gunma National College of Technology, Gunma 371-8530, Japan |
| Summary: | We derive the conditions under which dark energy models whose Lagrangian densities f are written in terms of the Ricci scalar R are cosmologically viable. We show that the cosmological behavior of f(R) models can be understood by a geometrical approach consisting in studying the m(r) curve on the (r, m) plane, where m=Rf_{,RR}/f_{,R} and r=-Rf_{,R}/f with f_{,R}=df/dR. This allows us to classify the f(R) models into four general classes, depending on the existence of a standard matter epoch and on the final accelerated stage. The existence of a viable matter dominated epoch prior to a late-time acceleration requires that the variable m satisfies the conditions m(r) approx+0 and dm/dr>-1 at r approx-1. For the existence of a viable late-time acceleration we require instead either (i) m=-r-1, (sqrt{3}-1)/2<m<1 and dm/dr<-1 or (ii) 0<m<1 at r=-2. These conditions identify two regions in the (r, m) space, one for the matter era and the other for the acceleration. Only models with a m(r) curve that connects these regions and satisfy the requirements above lead to an acceptable cosmology. The models of the type f(R)=alpha R^{-n} and f=R+alpha R^{-n} do not satisfy these conditions for any n>0 and n<-1 and are thus cosmologically unacceptable. Similar conclusions can be reached for many other examples discussed in the text. In most cases the standard matter era is replaced by a cosmic expansion with scale factor a propto t^{1/2}. We also find that f(R) models can have a strongly phantom attractor but in this case there is no acceptable matter era. |
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| Item Description: | Gesehen am 15.11.2017 |
| Physical Description: | Online Resource |